Maria has a total of $12,000 invested in two funds. The first fund pays simple interest at 6%
per year and the other pays simple interest at 7% per year. If the funds earn a combined
$817 in interest in one year, how much does she have invested in each fund?
Let's call the amount of money Maria has invested in the first fund "x" and the amount she has invested in the second fund "y".
We know that x + y = 12,000 (since that's the total amount of money she has invested).
We also know that the first fund earns 6% simple interest per year, so the amount of interest Maria earns on that fund is 0.06x. Similarly, the second fund earns 7% simple interest per year, so the amount of interest Maria earns on that fund is 0.07y.
We're told that the combined interest earned on both funds is $817:
0.06x + 0.07y = 817
Now we have two equations:
x + y = 12,000
0.06x + 0.07y = 817
We can use these equations to solve for x and y. Here's one way to do it:
1. Solve the first equation for one of the variables (let's say y):
y = 12,000 - x
2. Substitute this expression for y into the second equation:
0.06x + 0.07(12,000 - x) = 817
3. Simplify and solve for x:
0.06x + 840 - 0.07x = 817
-0.01x = -23
x = 2,300
So Maria has $2,300 invested in the first fund. To find the amount she has invested in the second fund, we can use the equation we found earlier:
y = 12,000 - x = 12,000 - 2,300 = 9,700
Therefore, Maria has $2,300 invested in the first fund and $9,700 invested in the second fund.
Let's assume Maria has invested x amount in the first fund, which pays 6% interest per year.
Therefore, she has invested (12000 - x) in the second fund, which pays 7% interest per year.
The interest earned from the first fund can be calculated as 6% of x, which is 0.06x.
Similarly, the interest earned from the second fund can be calculated as 7% of (12000 - x), which is 0.07(12000 - x).
The total interest earned from both funds is given as $817. So, we can write the equation:
0.06x + 0.07(12000 - x) = 817
Now, let's solve this equation step by step:
0.06x + 840 - 0.07x = 817
-0.01x = 817 - 840
-0.01x = -23
x = -23 / -0.01
x = 2300
Therefore, Maria has invested $2300 in the first fund (which pays 6% interest per year).
To find out how much she has invested in the second fund (which pays 7% interest per year), we can substitute the value of x into the equation:
12000 - x = 12000 - 2300
12000 - x = 9700
Therefore, Maria has invested $9700 in the second fund (which pays 7% interest per year).